Engineering Tripos Part IIA, 3D1: Geotechnical Engineering I, 2025-26
Module Leader
Lecturers
Prof G Madabhushi, Dr S Stanier
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Objectives
As specific objectives, by the end of the course students should be able to:
- Classify soils and assess their fundamental properties.
- Specify appropriate compaction criteria from soil laboratory data.
- Calculate vertical profiles of pore water pressure, total and effective stresses.
- Determine soil compressibility and calculate uniform ground settlements.
- Determine isochrones of excess pore pressure for 1D transient flows.
- Determine time-rate of consolidation and ground settlement.
- Specify “drained” or “undrained” direct shear tests, and interpret them.
- Use Mohr circles to interpret triaxial tests.
- Perform basic upper and lower bound limit analyses.
- Analyse limiting equilibrium with slip planes and slip circles as mechanisms.
- Search for the least optimistic mechanism of failure in soil.
- Perform simple design calculations of a strip footing on clay and sand.
- Perform basic estiamtes for the settlement of foundations
Content
Structures depend for their stability on the ground which supports their foundations. Furthermore, many structures are actually built of soil (road, rail and flood embankments, dams, road bases and rail beds, waste repositories) or have to retain soil as their prime purpose (basement walls, quay walls, tunnels and pipes). So all civil and structural engineers should understand soil behaviour and be able to apply this understanding in geotechnical engineering design and construction. This course introduces soil as a product of nature and focuses on its material properties and behaviour in engineering applications. Soil comprises solid grains, water and sometimes air. The solid phase is an interlocking aggregate of soil grains that can deform and rearrange. The fluid phase inhabits an interconnected pore space through which flow can take place. Total stresses, arising from loads and from the self-weight of the soil itself, have to be partitioned between these two phases. Pore pressures arise firstly from hydrostatics, but are modified by the effects of viscous drag when the fluid is flowing. Once pore pressures have been discounted, the remaining effective stresses must act between the grains, giving rise to deformations of the granular skeleton and therefore to displacements at the ground surface and possible distortions of any connected superstructures. This partition of stress is known as the principle of effective stress and is the key to understanding soil behaviour.
If loads or deformations are imposed on a saturated soil, whose pore fluid can therefore be regarded as incompressible, and if the loads are applied so quickly that fluid has no time to escape, then the process is described as undrained and the soil must deform at constant volume. If, on the other hand, the loads or deformations are imposed so slowly that the fluid can move completely freely, the process is described as drained and the soil deforms at constant pore pressure.The process of transient flow, taking soil from an undrained to a drained state, can lead either to consolidation (fluid drains out, and soil gets denser and stronger) or swelling.
In addition to being prone to volume changes, soils are also relatively weak in shear – perhaps three orders of magnitude weaker than concrete. Once again, the possibility of transient flow dictates the outcome. After large shear distortions, undrained soils ultimately display a constant undrained strength. In drained conditions, the strength of the soil is dictated by friction and interlocking between its grains. Ultimately the soil will display a constant internal angle of friction, familiar as the angle of repose of dry sand in sand dunes. Given enough time, underwater slopes in clay also rest at their angle of repose, as do sands. Tests to establish the drained (sand-like) or undrained (clay-like) strengths of soils, will be introduced and explained.
Once it has been established that a given undrained shear strength, or alternatively a given angle of internal friction, can be relied upon, the next step is to be able to make calculations to demonstrate whether a soil body will remain stable under applied loads, for example by a structural foundation. This module extends the plastic analysis of structures, first encountered in Part IB Structures, to bodies made of soil. Both “upper bound” style calculations based on assumed failure mechanisms, and “lower bound” calculations based on demonstrating equilibrium through Mohr’s circles, will be introduced.
Topic 1: The granular continuum
Basic definitions of soil constituents and their packing
Phase relationships. Density of grains and water; voids ratio and saturation; water content, unit weight. Classification of soils using particle size distribution curves; Relative density of sands. Consistency limit tests – plastic limit, liquid limit, and plasticity index of clayey soils.
Soils in nature and the principle of effective stress
Deposition and formation of natural soils. Loading history: normally consolidated and over-consolidated soils. The principle of effective stress. Stresses beneath level ground: total stresses, hydrostatic pore pressures, effective stresses. Water table, capillary zone.
Steady state seepage
Steady 1D flow through soil: seepage potential, hydraulic gradient, hydraulic conductivity
Topic 2: Compression and Compaction
Artificially formed soils: compaction
Compaction tests: compaction energy, dry density, optimum water content, degree of saturation. Controlling compaction in the field: tools and techniques, monitoring dry density, relative compaction. Brittleness and wetting-collapse of clayey soils if compacted dry of optimum, softness if compacted wet of optimum.
Compressibility and stiffness
Uniaxial compression of a skeleton of elastic, crushable grains by voids migration. Oedometer test, ultimate drained data of compression versus effective stress. Compressibility and stiffness of clays and sands.
Topic 3: Consolidation
Transient flow & the oedometer test
Excess pore pressures due to 1D loading. 1D consolidation of a unit cell with single drainage: the use of isochrones to describe transient flow. Interpreting transient compression in oedometer tests: consolidation parameters. Time-rate of consolidation for normally consolidated and overconsolidated soils (including swelling). Creep.
One-dimensional consolidation in the field
Using representative oedometer data to assess field settlements and time-rate of settlement. Application to land reclamation. Use of surcharging to reduce consolidation times. Consolidation due to changes in the groundwater regime.
Topic 4: The shear strength of soil
“Direct” and “simple” shear tests: undrained and drained
Direct/simple shear test. “Drained” tests at constant effective normal stress. Dilation / contraction to a critical state, mobilised angles of friction and of dilatancy; typical data of a sand and a clay. Residual friction of polished slip surface in pure clay.“Undrained” tests at constant volume; typical data of a sand and a clay. Limiting shear speeds for drained and undrained behaviour in a shear box test.
Topic 5: Limiting equilibrium of geotechnical structures
Shallow foundation design in clay : vertical loading
Bearing capacity of a shallow strip footing on clay. Upper bounds; kinematically admissible mechanism, shear strength, global work or equilibrium. Slip circles and slip planes for non-dilatant soils. Lower bounds; statically admissible stress field, shear strength, equilibrium everywhere. Uniform undrained shear resistance.
Shallow foundation design in sand : vertical loading
Bearing capacity of a shallow strip footing on sand. Uniform angle of friction; stress discontinuities, dry sand. Weightless soil. Upper and lower bounds.
Settlement of foundations
Boussinesq's solution. Stresses beneath a loaded area. Settlement prediction for shallow foundations
Examples papers
There will be three examples papers directly related to the lecture course, given out in weeks 1, 3 and 6 on the following topics:
- Basic relationships for a granular continuum
- Consolidation and swelling
- Soil strength, and the limiting equilibrium of soil bodies
Coursework
Atterberg Limit Tests
Learning objectives:
- Determine the water content of a soil
- Determine the liquid limit of fine-grained soils
- Determine the plastic limit of fine-grained soils
- Classify soils
- Assess the strength of soils at tje liquid limit
Practical information:
- Sessions will take place in the Structures Research Laboratory, during the first 3-5 weeks of the term
- Sign up for laboratory sessions will be on moodle, as advertised on the site.
- This activity involves a preliminary quiz, available on the moodle site, to be completed prior to the laboratory session
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/06/2025 13:18
Engineering Tripos Part IIA, 3C9: Fracture Mechanics of Materials & Structures, 2025-26
Module Leader
Lecturers
Prof N.A. Fleck, Prof V.S. Deshpande
Lab Leader
Dr G McShane
Timing and Structure
Lent term. 16 lectures + coursework
Prerequisites
3C7 assumed
Aims
The aims of the course are to:
- Explain the physical processes underlying fracture from a single dominant crack and from a distribution of cracks.
- Describe the main concepts of fracture mechanics in terms of stress analysis, failure mechanisms and design methods.
- Discuss both linear elastic fracture mechanics (LEFM) and ductile fracture.
- Apply the methods to a wide range of engineering applications from thin film design in electronics to fatigue life assessment of nuclear pressure vessels and damage mechanics of concrete.
Objectives
As specific objectives, by the end of the course students should be able to:
- To explain the physical processes underlying fracture from a single dominant crack and from a distribution of cracks.
- Quantitative design methods are physically based and used to predict fatigue life and residual strength of damaged structures
Content
Elastic stress analysis (4L) Prof. Deshpande
- Williams solution using the Airy stress function
- LEFM and interfacial fracture
- Energy appraoch to fracture
- Practical K-calibrations and use of superposition
- Fracture of thin films and of weldments
- Prediction of fracture toughness
Small Scale Yielding (2L) Prof Deshpande
- plastic zone size and crack tip opening displacement
- R-curves: the tear resistance of metals, composites and biological tissues
Large Scale Yielding (5L) Prof Fleck
- Dugdale model for a large plastic zone from a crack tip, and transition to bulk plasticity
- Application to adhesive joints and crazing of polymers, and to pressure vessels
- Void nucleation and growth in a plastic field
Fatigue crack growth (5L) Prof Fleck
- Threshold, Paris law, variable amplitude loading for aircraft
- S-N curves for fatigue crack initiation and growth
REFERENCES
Fracture Mechanics: fundamentals and applications, T.L.Anderson,Taylor Francis,2005.
Coursework
Learning objectives:
(i) To develop an understanding of failure process under monotonic loading at ambient temperatures
(ii) To examine the use of stress intensity factor and strain energy release rate to describe the failure of cracked bodies.
(iii) To evaluate the use of linear elastic fracture (LEFM) and the concept of limit load in the assessment of cracked components.
Practical information:
The course work involves:
- Lab Session 1 - Tensile testing (1.5 hrs), location: Fatigue Laboratory, ground floor, Baker Building
- Lab Session 2 - Pipe bursting (30 mins), location: Materials Teaching Laboratory, ground floor, Inglis Building
- Feedback session
Further information, including a link to book lab sessions, is available on the 3C9 Moodle page.
Full Technical Report:
Students have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 16/01/2026 12:27
Engineering Tripos Part IIA, 3C8: Machine Design, 2025-26
Module Leader
Lecturers
Prof M Sutcliffe, Dr R Roebuck, Dr X Na
Lab Leader
Timing and Structure
Michaelmas term.16 lectures.
Aims
The aims of the course are to:
- Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
- Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
- To analyse the behaviour of multiple gear drives and planetary gears.
- Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
- Apply the principles of power matching to hybrid drives.
- Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.
Objectives
As specific objectives, by the end of the course students should be able to:
- Calculate the strength limitations of solid contacts.
- Analyse the kinematical behaviour of contacts, especially in rotating machinery.
- Understand and analyse the performance of friction drives.
- Be familiar with the geometry and kinematics of involute gear wheels and racks.
- Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
- Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
- Understand how power transmission components are used as part of a system, including hybrid drives.
- Determine the operating point and calculate the optimum speed ratio for specified conditions.
- Select a rolling element bearing for a specific duty.
Content
Mechanics of contacts (5L) Dr Richard Roebuck
- Hertzian point contacts
- Stresses and stiffness
- Hertzian line contacts
- Applications in bearings and CVTs
- Traction drives and CVTs
Gears (6L) Prof. Michael Sutcliffe
- Geometry and kinematics
- Failure, root bending and contact fatigue
- Design and applications
- Multiple drives and planetary gears
- Design calculations for planetary gears
Power matching (3L) Dr Xiaoxiang Na
- Introduction and applications: automotive transmission, bicycle transmission
- Sources and loads; devices and their characteristics
- Power matching using a simple gear ratio
- Hybrid drives
Rolling element bearings (2L) Dr Xiaoxiang Na
- Bearing types; life equation
- Shaft and bearing arrangements
Examples papers
Examples Paper 1 - Mechanics of contacts (issued at lecture 1)
Examples Paper 2 - Gears (issued at lecture 6)
Examples Paper 3 - Power matching, rolling element bearings (issued at lecture 12)
Coursework
Power output characteristic of a cyclist
In this experiment the power output charateristic of a cyclist will be determined by holding the heart rate (a proxy for power input) constant and determining the dependence of crank torque and crank power on crank speed.
Learning objectives:
- to calibrate and operate instrumentation to measure human power output
- to propose and test an hypothesis using measured data with large inherent uncertainty
- to understand the power output characteristic of a cyclist
Practical information:
- Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8 (Fridays and Wednesdays, 11am-1pm)
- This activity does involve preliminary work, approximately 40 minutes: read the lab sheet carefully and watch the demonstration video before the session.
- Book a timeslot online via the moodle site.
- The practical needs to be done in pairs, with at least one member of the pair being comfortable riding the stationary bicycle. It is not possible to perform the experiment individually.
- The lab report must be written individually. All data processing, analysis and interpretation performed after the lab session must be done independently and not in collaboration with each other or anyone else.
Full Technical Report:
Students will have the option to submit a Full Technical Report. The FTR should be a complete, detailed, formal report of the experiment, suitable for publication in an engineering journal. It should include all of the information necessary for the reader to understand the aim, objectives, apparatus, method, results, analysis, discussion and conclusions. In addition the FTR should describe in precise engineering terms the operating principles of three different commercially-available devices for measuring cyclist power output, and comment upon likely sources and magnitudes of error.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 04/06/2025 13:18
Engineering Tripos Part IIA, 3C6: Vibration, 2025-26
Module Leader
Lecturers
Prof D Cebon, Dr T Butlin
Lab Leader
Timing and Structure
Michaelmas term. Vibration of Continuous Systems: 1 lecture/week, weeks 1-8 Michaelmas term (Dr T Butlin), Vibration of Lumped Systems: Rayleigh's method, 1 lecture/week, weeks 1-8 Michaelmas term (Prof D Cebon). 16 lectures.
Aims
The aims of the course are to:
- Introduce the central ideas and tools for the analysis of small (linear) vibration in mechanical systems.
- Introduce simple continuous systems which may be combined as components of larger systems.
- Introduce the general approach to lumped systems via mass and stiffness matrices, and the resulting properties of vibration modes and their frequencies.
Objectives
As specific objectives, by the end of the course students should be able to:
- Derive the partial differential equations governing the forced or free motion of uniform one-dimensional systems.
- Use these equations and appropriate boundary conditions to obtain vibration modes and natural frequencies.
- Analyse continuous systems using modal methods.
- Compute impulse and harmonic response by modal and direct methods.
- Be able to derive the dispersion relation for wave propagation in 1D structures.
- Understand that vibration can be expressed in terms of wave propagation or superposition of modes.
- Calculate the response of a coupled system from a knowledge of the responses of the separate subsystems.
- Apply Rayleigh's method to continuous systems.
- Take advantage of the link between Lagrange's equations and small vibration.
- Explain the concept of a vibration mode, and be able to find the modes and their natural frequencies by an eigenvector/eigenvalue calculation.
- Understand orthogonality of modes, modal damping, modal density and modal overlap factor.
- Express the frequency response functions or the impulse response functions of a system in terms of the normal modes, and be familiar with the concepts of resonances and antiresonances.
- Recognise and apply the reciprocal theorem for responses.
- Use the stationary property of normal mode frequencies to estimate frequencies given assumed mode shapes, using minimisation with respect to any free parameters.
Content
This course aims to present a systematic approach to the study of small vibration of engineering components and structures. The course picks up where Part IA Linear Systems and Vibration left off. Concepts which were barely discussed (e.g. reciprocity and the orthogonality of vibration modes) are important for building up qualitative insights into vibration behaviour. Alongside the mathematical tools for quantitative analysis the course offers vital ingredients for an engineer's education.
Vibration of Continuous Systems (8L)
- Vibration of strings; axial and transverse vibration of beams, torsional vibration of circular shafts; 1D acoustic vibration in a duct;
- Modal analysis of simple systems;
- Wave-based analysis of vibration, including D'Alembert's solution;
- Dispersion relation for travelling waves;
- Response to impulse and harmonic excitation;
- Transfer functions and the meaning of poles and zeros;
- Coupling of systems;
- Rayleigh's method for continuous systems.
Vibration of Lumped Systems (8L)
- Application of Lagrange's equations to small vibrations; undamped vibration of systems with N degrees of freedom;
- Matrix methods and modal analysis;
- Response functions in frequency and time domains; properties of frequency-response functions; reciprocal theorems;
- Modal damping and modal overlap;
- Rayleigh's method for discrete systems.
Coursework
A data-logging and FFT analysis system is used to measure the frequency response of a vibrating system by three different methods, to compare their merits and disadvantages.
[Coursework]
Learning objectives:
- To investigate alternative methods of determining calibrated frequency response transfer functions of a mechanical vibrating system, using a digital measuring system;
- To predict the response of a system from measured responses of its decoupled subsystems, and to compare with the measured response of the coupled system.
Practical information:
- Sessions will take place in the South Wing Mechanics Laboratory, throughout Lent term.
- This activity doesn't involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 04/06/2025 13:18
Engineering Tripos Part IIA, 3C5: Dynamics, 2025-26
Module Leader
Lecturers
Prof H.E.M. Hunt, Dr A Cicirello
Lab Leader
Timing and Structure
Lent term, 16 lectures. Introduction and Rigid-body Dynamics: 2 lectures/week, weeks 1-5 (Prof H E M Hunt); Lagrangian Mechanics: 2 lectures/week, weeks 6-8 (Dr A Cicirello)
Aims
The aims of the course are to:
- Introduce the ideas and methods of 3D dynamics: the motion of rigid bodies in three dimensions under given forces and moments.
- Introduce the Lagrange and Hamiltonian formulations of mechanics.
- To show how to apply these methods in a straightforward way to a wide range of problems.
Objectives
As specific objectives, by the end of the course students should be able to:
- Represent the inertia of a rigid body by an inertia matrix, be able to calculate the moments and products of inertia for simple shapes, be able to find the principal axes of inertia.
- Derive Euler's equations for the motion of a rigid body under prescribed moments.
- Apply these equations to the motion of symmetrical rotors, to explain the phenomena of precession, nutation and the rate gyroscope.
- Analyse simple problems involving the rolling of rigid bodies, for example a spinning penny on a table.
- Explain the concepts of generalised coordinates and generalised forces.
- Express the kinetic and potential energies of a system in term of the generalised coordinates, and to use these to obtain Lagrange's equations of motion.
- Approximate the kinetic and potential energies by quadratic forms, and hence deduce the mass and stiffness matrices for small vibration of a system about its equilibrium position.
- Explain the concept of generalized momentum and show how the Hamilton's equations can be used to find the equations of motion.
- Explain the concepts of Poisson brackets, conserved quantities, and canonical transformations.
Content
This module aims to present a systematic approach to the study of dynamics. Once the main techniques have been grasped, a very wide range of problems can be tackled with confidence. The first part of the course presents the tools required to analyse rigid-body motion in three dimensions. These are necessary for a proper understanding of gyroscopic systems, inertial navigation, satellites in space and the stability of high-speed rotating systems such as turbines and compressors.
The second part of the course deals with Lagrangian and Hamiltonian mechanics, a systematic way to formulate dynamical problems using energy functions.
Introduction and Rigid-body Dynamics (10L)
- Equations of motion of a rigid body in three dimensions.
- The inertia tensor; principal axes.
- Gyroscopes and their application.
- Problems involving rolling bodies.
Lagrangian and Hamiltonian Mechanics (6L)
- Lagrange's equations; connection to Newton's laws; generalised coordinates and generalised forces.
- Applications to a range of problems.
- Hamilton's equations, Poisson brackets, conserved quantities, canonical transformations.
- Example applications.
Coursework
Gyroscopic Phenomena
Learning objectives:
- To observe gyroscopic effects and to compare these observations with theory;
- To discover some of the engineering applications of gyroscopes;
- To develop a physical understanding of gyroscopic phenomena.
Practical information:
- Sessions will take place in the South Wing Laboratory, during weeks 1-7.
- This activity doesn't involve preliminary work.
- The lab can be completed in two hours
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 05/06/2025 18:53
Engineering Tripos Part IIA, 3C1: Materials Processing & Design, 2025-26
Module Leader
Lecturers
Dr M Seita, Dr C Barlow
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Provide an understanding of materials processing technology for the manufacture of products.
- Consider the integrated nature of design, material and processing in the manufacture of products.
- Illustrate the processing factors that influence selection in design.
- Relate processing to microstructure evolution and product failure.
Objectives
As specific objectives, by the end of the course students should be able to:
- Have a broad appreciation of the different materials processing methods used for metals, ceramics, polymers and composites.
- Understand the main interactions between process and material in design and process selection, for each of the main classes of material.
- Understand the factors which control the microstructure of shaped castings, and their consequences for final properties and design for casting.
- Know the main classes of polymers and composites, and understand the processing and design considerations in selecting these for a given component.
- Know the main deformation processes for wrought alloys, and be able to conduct simple upper bound analysis of plastic deformation.
- Know the microstructural characteristics of wrought alloys, and the reasons for alloying and heat treatment, with examples from Al alloys and steels.
- Understand hardenability of steels, using CCT diagrams to select steels and heat treatments for a given component specification.
- Understand the processes and issues in the manufacture of powder metallurgy and ceramic products.
- Understand the importance of surface treatments and joining technologies, and know the main factors to consider in process selection.
- Appreciate the current potential and limitations of additive manufacturing methods.
- Be able to apply their knowledge of materials processing, microstructure evolution, and the mechanisms of material degradation to analyse and predict failures and to improve product design.
Content
Introduction (1L, Dr M Seita)
- Classification of manufacturing processes.
- Coupled problems in design and manufacturing: the interaction between material, process and design parameters.
Metal Casting (2L, Dr M Seita)
- Ingot and shaped casting technology.
- Revision of phase diagrams and transformations applied to solidification: segregation, constitutional supercooling, casting alloys and microstructures.
- Casting defects and design of shaped castings.
Deformation Processing of Wrought Alloys, Heat treatment (2L, Dr M Seita; 2L, Dr G McShane)
- Revision of phase transformations and TTT diagrams.
- CCT diagrams and hardenability for steels.
- Wrought alloy processing and microstructure evolution.
- Simple modelling of plastic forming processes (upper bound method).
- Application of plasticity analysis to rolling, forging, extrusion, machining of metals; case studies.
Powder Processing, Processing of Polymers and Composites (3L, Dr C Barlow)
- Sintering, HIPing and other processing technologies for powder metals and ceramics.
- Polymer and composite processing technology.
- Design, material and process selection for polymers and composites.
Surface Engineering, Additive Manufacturing, Joining and Welding (3L, Dr M Seita)
- Surface engineering processes and their applications.
- Welding technology (fusion, friction, laser, ultrasonic), and other joining processes (mechanical, adhesives).
- Selection of surface engineering and joining processes in design.
- Additive manufacturing (AM) methods and their current potential.
Design against Failure (3L, Dr C Barlow)
- Processing as the origin of defects and failures (microstructure, damage, residual stress).
- Environmental factors in failure of materials.
- Analysis and case studies of failures.
Further notes
This module also runs in the MANUFACTURING ENGINEERING TRIPOS PART IIA - Module 3P1: Materials into Products.
Supervisions will be by a combination of conventional groups and larger examples classes.
Examples papers
0. Revision (Phase Diagrams etc)
1. Metal Casting, Heat Treatment of Steels, Microstructure in Wrought Alloy Processing
2. Modelling of Wrought Alloy Processing
3. Powder Processing, Polymers, Polymer Composites, Surface Engineering, Additive Manufacturing, Joining and Welding, Design against Failure
Coursework
Laboratory: Jominy end-quench test for hardenability
Learning objectives:
- To understand and conduct a Jominy end quench for steels, measuring and comparing hardness profiles for plain carbon and alloy steels
- To correlate microstructure along the sample with the hardness profiles
- to be able to interpret CCT diagrams for the same steels, and assess their accuracy against experimental data
Practical information:
- Sessions will take place in the Materials Lab, during weeks 2-6.
- Students are expected to read the handout in advance of their booked session.
- Practical activity covers a single Jominy end-quench, hardness traverses on two samples (one per pair, pooling the data), observation of microstructures on the two steel samples
Full Technical Report: Weldability of steels, and correlation with hardenability
Students will have the option to submit a Full Technical Report.
A separate document is issued containing:
- 3 point bend test data for welded and unwelded samples of 3 steels
- images of the failed 3 point bend samples
- micrographs from the weld regions in all three steels, with selected hardness data
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D2
Understand customer and user needs and the importance of considerations such as aesthetics.
D3
Identify and manage cost drivers.
S1
The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.
S3
Understanding of the requirement for engineering activities to promote sustainable development.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
P7
Awareness of quality issues.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 28/09/2025 10:46
Engineering Tripos Part IIA, 3B6: Photonic Technology, 2025-26
Module Leader
Lecturer
Dr Q Cheng, Prof R Penty
Lab Leader
Dr Q Cheng,
Timing and Structure
Lent term. 16 lectures.
Aims
The aims of the course are to:
- Introduce key aspects of photonics technology and its applications in fields such as communications, storage, medicine, environmental sensing and solar power.
- Introduce both optical fibres and photonic components including light emitting diodes, lasers, photodiodes and solar cells.
- Introduce photonic sub-systems including transmitters and receivers for use in applications such as wide area, metropolitan and local area networks.
Objectives
As specific objectives, by the end of the course students should be able to:
- Know of the main applications of optoelectronics.
- Choose appropriate transmission media with reference to bandwidth and physical environment.
- Know which semiconductors are used for what optoelectronic tasks and why.
- Be familiar with the construction of LEDs, and be able to estimate their linewidth, speed and external quantum efficiency.
- Be familiar with the construction of Fabry-Perot and grating based diode lasers, and how this relates to their spectra and light-current characteristics
- Estimate the response of semiconductor lasers to changes in their drive current or operating environment.
- Be familiar with the construction of junction photodiodes, and hence be able to estimate the capacitance and responsivity, and know how to operate them for best sensitivity and speed.
- Be familiar with the relationship in construction and operation between junction photodiodes, avalanche photodiodes, solar cells and photoconductors.
- Perform noise calculations for typical optoelectronic circuits.
- Be aware of the design of typical receiver circuits with reference to the physical characteristics of photodetectors.
- Be familiar with the construction of fibres as well as the causes of attenuation and dispersion.
- Perform calculations of link budgets, dispersion and attenuation limits.
Content
Photonic Technology
- How and why optoelectronics fits within electronics: Outline of major applications areas within engineering, science and medicine. Examples of optoelectronic subsystems, solar cells, lighting, Communication transceivers.
- Optical processes in semiconductors: Direct and indirect band structures, comparison of Silicon, Germanium, GaAs based and InP based materials. Optical absorption, Optical emission, non-radiative transitions
- Light emitting diodes: Quantum efficiency, wavelength, optical line width, visible devices, modulation limits, device structures, materials.
- Laser diodes: Stimulated emission, optical gain. Laser as a feedback amplifier of spontaneous emission, Fabry-Perot laser cavities. Rate equations, modulation characteristics, dynamic linewidth. Examples of common diode laser types.
- Optical transmitter circuits: LED based circuits, LED types, transmitter power, bandwidth. Laser based circuits, laser types, biassing, feedback circuits. Noise in optical systems, shot noise, thermal noise, noise bandwidths, circuit effects.
- Photodetectors: PN junction photodiodes, photoconductors, solar cells, avalanche photodiodes, capacitance, transit time, leakage currents, avalanche gain and noise.
- Optical receiver circuits; Transimpedance amplifiers.
- Fibres and transmission: Multimode and single mode fibres: Attenuation, dispersion, interfaces to fibre.
- Transmission systems in a real environment: Power budgets, error rates, monitoring, power penalties, margins for temperature and ageing. Emerging technologies.
Examples papers
Three examples papers are provided during the course.
Coursework
Laser Experiment
Students are provided with two types of semiconductor lasers and are asked to perform basic electrical and optical measurements to characterise their operation. The measurements are used to derive the basic properties of these laser devices and understand the underlying fundamental physical mechanisms that govern their operation.
Learning objectives:
After completing this coursework students should be able to
- Be familiar with the basic operation of LEDs and lasers,
- Generate light-current and current-voltage curves for a semiconductor device,
- Find the laser threshold and stray series resistance of a laser,
- Characterise the spectrum of light emitted from LEDs and lasers,
- Estimate the refractive index of the laser.
Practical information:
- Sessions will take place in EIETL, during weeks 3-8 in Lent term and weeks 1-2 in Easter term.
- This activity involves preliminary work (~ 2 h): you should read the related lecture notes and experiment information sheet with the appendices, to gain some knowledge background on semiconductor devices and error analysis prior to experiments.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 04/06/2025 13:16
Engineering Tripos Part IIA, 3B5: Semiconductor Engineering, 2025-26
Module Leader
Lecturers
Prof S Hofmann, Prof A Ferrari
Lab Leader
Prof S Hofmann
Timing and Structure
Michaelmas term. Weeks 1-4 (Prof a Ferrari), Weeks 5-8 (Prof S Hofmann). 16 lectures in total with 2 lectures per week. In-person lectures will be recorded (although the quality of the recording cannot be guaranteed).
Aims
The aims of the course are to:
- Provide a framework of basic semiconductor physics
- Demonstrate how semiconductor physics dictates the operation and performance of electronic devices in circuits and systems.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the concept of wave-particle duality especially with regard to electrons.
- Calculate allowed electron energy levels in single atoms from solutions of Schrodinger Equation, and be familiar with the concept of energy bands.
- Explain electron behaviour in energy bands.
- Be familiar with the idea of the Fermi level, and the formation of n and p type semiconductors by the deliberate addition of dopant atoms.
- Apply the continuity equation to different semiconductor problems.
- Explain the formation of p-n junctions, and be familiar with how current flow across the junction is limited by minority carrier flow.
- Know how p-n junction formation can be used in the design of JFETs and bipolar transistors.
- Compare and contrast the performance of JFET and bipolar Transistors.
- Know how metal semiconductor junctions can be used in the design of MESFETs and HEMTs, and be able to compare operation with that of the JFET.
- Explain the operating modes of a MOS Capacitor and MOSFET, and be familiar with how device design affects I-V characteristics.
- Understand how MOSFETs may be utilised as simple memory devices.
Content
Quantum Mechanics and Semiconductor Physics
- Introduction to quantum mechanics: wave-particle duality, Schrodinger’s equation
- Physics of semiconductors: E-k diagrams, energy bands, direct and indirect band gaps, density of states, Fermi level, intrinsic and extrinsic semiconductors, drift and diffusion, recombination and generation, continuity equation
Semiconductor Devices
- Basic junctions and heterostructures: p-n junctions band diagrams, junction in equilibrium, current flow in p-n junction, metal-semiconductor junctions, heterojunctions
- Device engineering: the bipolar junction transistor (BJT), the heterojunction bipolar transistor (HBT), the junction field effect transitor (JFET), the metal semiconductor field effect transistor (MESFET), the high electron mobility transistor (HEMT) and the metal oxide semiconductor field effect transistor (MOSFET) - how they operate and I-V characteristrics
Examples papers
Four examples papers are provided during the course, covering lectures 1-4, lectures 5-8, lectures 9-12 and lectures 13-16.
Coursework
Schottky Barrier Diode
Learning objectives:
- Experimentally probe semiconductor engineering concepts related to theory given in lectures.
- Use oscillator circuit to investigate voltage dependence of the capacitance of a Schottky barrier diode and understand how this is a powerful technique for characterisation of semiconductor doping.
- Compare the current-voltage characteristics of Schottky and p-n diodes and explore deviations from ideal diode behaviour.
Practical information:
- Sessions will take place in the EIETL, during weeks 1-8 of Michaelmas term.
- This activity involves preliminary work (read and understand the lab handout).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 04/06/2025 13:16
Engineering Tripos Part IIA, 3B4: Electric Drive Systems, 2025-26
Module Leader
Lecturers
Prof T Long, Prof T Coombs
Lab Leader
Timing and Structure
Lent term. 16 lectures.
Aims
The aims of the course are to:
- Build on the Electrical Power Course given in Part 1B.
- Recognise that electrical motor drives in applications of all kinds are required to perform at high efficiency, controllability and reliability.
- Study electric drives for: medium power applications; precision applications; high power transport and industrial applications; domestic applications.
- Understand permanent magnet motors and their drive systems with a special focus on all-electric vehicles.
- Examine the magnetic design of permanent magnet motors, focusing on soft magnetic and permanent magnetic materials, saturation and iron losses.
- Study stepper motors which are used in robotics, 2-D and 3-D printers.
- Understand the main design principles of large three-phase induction motors.
- Study electric drive systems based on three-phase induction motors.
- Examine mechanisms for heat production and removal in electrical machines, and be able to carry out thermal analysis for duty-cycling operation.
- Study single-phase induction motor drive systems which are dominant in domestic applications such as white goods.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand the basic principles of operation.
- Be able to apply simple motor design rules.
- Be able to specify diffferent motors for different applications.
- Understand the design contstriants on multiple motor machines.
- Appreciate magnetic and thermal constraints.
- Be aware of different magnet materials and suitability for motor operation.
Content
The subject of electric drive systems is a vast one, and so the syllabus has been designed to give the student an appreciation of this very important area of engineering by focusing on four areas: electric drives for medium power applications such as electric vehicles (drives based on permanent magnet motors); automation drives with applications such as robotics, 3-D printers (based around stepper motors); large drives for transport/industry (based around the three-phase induction motor); domestic drive systems based around the single-phase induction motor. The course illustrates the idea that the engineering of electric drive systems is multidisciplinary, involving an understanding of mechanics, control systems, power electronics, electromagnetics for machine design, electrical materials and thermal design.
Introduction to Electric Drive Systems (1 lecture)
What is an electric drive system? Range of applications. Components of a drive system. Drive based around brushed DC motor: DC motor principles and operating characteristics; sensors; mechanical load; controller; power electronic converter.
Permanent magnet machines (4 lectures)
Brushed permanent magnet machines and drive systems; principles of operation; analysis; transient behaviour and electrical/electromechanical times constants.
Trapezoidal brushless DC motors: construction, theory and operation as an electric drive system; sensored and sensorless operation.
Sinusoidal brushless DC motors: construction, theory and operation; electric drive system and control; application.
All-electric vehicle: an examination of the specificationof the electric drive system of the NissanLeaf. How the main design choices are made. Consequences for range, top speed, acceleration, efficiency and CO2 emissions.
Magnetic design (1 lecture)
Characteristics of soft and permanent magnetic materials. Analysis using magnetic circuits. Iron loss calculations. Designing with permanent magnet materials.
Stepper motors (2 lectures)
Construction, theory of operation and analysis. Position error. Torque-position characteristic and oscillatory behaviour and its avoidance. Operation at speed and when accelerating. Commissioning. Types of excitation: full-stepping, half-stepping, micro-stepping. Drive circuits.
Basic machine design (2 lectures)
Stator structure including winding and core. Electrical and magnetic loadings. Machine ratings and basic requirement specification. Basic machine design procedure and process.
Induction machine operation (2 lectures)
Operatingcharacteristics of induction machine. Maximum torque and starting torque of induction machines. Speed control methods of induction machine: adjusting stator voltage, adjusting rotor resistance, variable voltage variable frequency (VVVF) method.
Thermal duty cycle of electric machines (2 lectures)
Temperature expression and thermal analysis of electric machines. Basic cooling methods and over temperature protection of electric machine.
Single phase induction machine and universal AC machine (2 lectures)
Theory and equivalent circuit of single phase induction machines. Operating characteristics of single phase induction machines. Equivalent circuit of universal AC machines. Typical applications of universal AC machines.
Examples papers
4 examples papers issued at 2 week intervals to coincide with the lecture material.
Coursework
Electric drive for vehicles
Aim: To understand how an electrical drive system based around a brushless DC motor functions, and to investigate its performance.
Learning objectives:
-
To characterise the components of the drive system through a series of tests.
-
To perform experiments on the drive system under steady-state conditions in order to understand how it works, and to compare experimental results with theory.
-
To investigate the transient behaviour of the drive system during typical drive-cycles.
Practical information:
- Sessions will take place in the EIETL during the Lent term.
- It is best to do the lab after lecture 5 so that all of the background material has been covered.
- Prepare for the lab by reading the lab handout and going over lectures 1 - 5.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 05/06/2025 13:45
Engineering Tripos Part IIA, 3B3: Switch-mode Electronics, 2025-26
Module Leader
Lecturer
Prof S Goetz, Prof T Long
Lab Leader
Prof T Long
Timing and Structure
Michaelmas term. 2 lectures/week.
Prerequisites
2P5
Aims
The aims of the course are to:
- Introduce power electronics and some of its main applications (power conversion in renewable energy, electric vehicles, power supply unit (PSU))
- Introduce typical topologies for AC-DC, DC-DC and DC-AC power conversion
- Give basic and useful skills in analysing and designing power electronics based power converters (PLECS modelling)
Objectives
As specific objectives, by the end of the course students should be able to:
- Know typical applications and requirements of power electronic based power converters (switch-mode power conversion)
- Know the characteristics of the diodes and power transistors and their functions in switch-mode power electronic circuits
- Know the functions of inductors and capacitors in switch-mode power conversion
- Know typical switch-mode power conversion circuit topologies: DC-DC, DC-AC, AC-DC
- Know how to reduce voltage and current ripple using smoothing circuits.
- Know high frequency transformers and their functions in power converters
- Understand the principle of pulse-width modulation and simple ways of generating pulse-width modulated waveforms.
- Know the structure and working principle of MOSFET, BJT, and IGBT as power transistors
- Describe various losses and estimate the efficiency of a power electronic system.
- Gain skills of power electronic system modelling (PLECS)
- Conduct basic tests of power electronic systems and use digital oscilloscope, pulse generator, probes and be familiar with typical power electronic and passive component devices and packages in real systems (via Lab)
Content
This module will also introduce PLECS modelling, all module students are offered free license (full function) of PLECS for 12 months.
Lecture 1: Introduction of power electronic systems and their applications, common math and physics used in analysing power electronic systems
- Non-isolated DC-DC converter
Lecture 2: Non-isolated DC-DC converters (BUCK, BOOST and BUCK-BOOST) in Continuous Current Mode (CCM) their operating principles
Lecture 3: Non-isolated DC-DC converters in Discontinuous Current Mode (DCM) their operating principles
- Bridge based DC-AC inverter/rectifier
Lecture 4: Bridge converter, the circuit, working principle and applications
Lecture 5: Single phase DC-AC inverter and Sinusoidal Pulse Width Modulation (SPWM)
Lecture 6: Three phase DC-AC inverter/rectifier and AC line filter design
Lecture 7: Tutorial 1: DC-DC and DC-AC converters (two Tripo level questions)
- Diode based AC-DC rectifier
Lecture 8: Uncontrolled single AC-DC rectifier with ideal AC source, diode bridge circuit and principles, capacitor filtering techniques
Lecture 9: Uncontrolled three AC-DC rectifier with ideal AC source, diode bridge circuit and principles, capacitor filtering techniques
- Isolated DC-DC converter
Lecture 10: Isolated DC-DC converter: high frequency transformers, push-pull converter
Lecture 11: Flyback DC-DC converter: working principles and design requirements
Lecture 12: LLC Resonant converter: working principles and design requirements
Lecture 13: Tutorial 2: AC-DC diode based rectifier and isolated DC-DC converters (Flyback and LLC Resonant)
- Power electronic devices
Lecture 14: Power diodes and bipolar junction transistor
Lecture 15: The Insulted Gate Bipolar Transistor (IGBT): modes of operation. trade-offs.
Lecture 16: The power MOSFET: Concept, modes of operation. trade-offs.
Examples papers
4 examples papers issued at 2 week intervals to coincide with the lecture material.
Coursework
DC-DC converter (upgraded new lab kit and facility from 2020)
Objectives:
- Be familiar with real power electronic and passive devices and their packages
- Use digital oscilloscope for power electronic system testing and data acquisition
- Use voltage and current probe of measuring switching voltage and current
- Observe and operate Pulse Width Modulation (by pulse generator) of controlling power electronic system
- Observe and operate passive components in power electronic systems and understand their functions
Pre-requisite
- Watch introductory video prior lab
- Read lab sheet prior lab
Full Technical Report:
- Optional tasks and questions are given for FTR
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 04/06/2025 13:16
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